Why does 'Knife Project' only sometimes select the new faces?
It depends on whether the object you are using as the 'knife' is 'closed' or not. In your first image the circle is a closed loop of edges, so everything inside is selected. In your second image the two edges are not connected so the result of the knife project is not selected.

Closed edges:



Open edges:



If you want the result to be selected then make sure the object you are using as the 'knife' is a closed loop of edges.

I don't 100% understand why this is the case, it could be a technical limitation or done by design.